Hi Kevin,
Thank you for your message.
Unfortunately, Catholic records in Donaghmoyne only begin in 1841 so you will not be able to find records for the children born before then or birth/marriage records for Thomas and Bridget.
http://www.irishtimes.com/ancestor/fuses/rcparishmaps/index.cfm?fuseaction=showidrecords&CityCounty=Monaghan&parish=Donaghmoyne&churchid=304
The above link also shows where copies of available records are.
You could try looking for record of the family in the land records pertaining to Ireland in the 19th century. This does not offer any genealogical information but it may give you some names as a starting point to your research.
You could also check for record of the family in the land acts pertaining to Ireland in the 19th century. There are two:
The Tithe Applotment Books (1823-1838) found at http://titheapplotmentbooks.nationalarchives.ie/search/tab/home.jsp
and Griffith?s Valuation (1848-1864) found at http://www.askaboutireland.ie/griffith-valuation/
Some other websites that may be useful to you are:
The National Archives of Ireland http://www.nationalarchives.ie/genealogy1/genealogy-records/introduction/
The National Library of Ireland http://www.nli.ie/en/family-history-introduction.aspx
The National Archives UK ? genealogy search: http://www.nationalarchives.gov.uk/records/looking-for-person/
The Public Records Office of Northern Ireland http://www.proni.gov.uk/index/family_history.htm
Genealogy Links: http://www.genealogylinks.net/uk/ireland/monaghan/index.html
You could also try contacting Monaghan Genealogy for some assistance. However a fee may apply. Here are their contact details:
Monaghan Genealogy,
6 Tully,
Monaghan.
Email: theomcmahon@eircom.net
I hope some of these links are helpful. Please be patient - as our programme has only begun to rollout across the island of Ireland and volunteers in some areas may not yet be organized.
Kind regards,
Genealogy Support